1. Suppose that you generate 20 random samples from the integers {0,1, ., 9}. What are the mean and variance for the number of integers that do not appear in the 20 samples?
1. Suppose that you generate 20 random samples from the integers {0,1, ., 9}. What are the mean and variance for the number of integers that do not appear in the 20 samples?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
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![1. Suppose that you generate 20 random samples from the integers {0,1, ...,9}. What are the
mean and variance for the number of integers that do not appear in the 20 samples?
2. Let X be a Poisson random variable with parameter 2. Show directly (i.e. don't use the
moment generating functions) that E[X"] = AE[(X + 1)"=1). Use the result to compute
E[X®].
3. Recall (from HW5) the hazard rate:
fx(x)
hx(x) =
%3D
1– Fx(x)'
Suppose that X is a continuous random variable with density
fx(x) = ade-* + (1 – a)µe¬#x, for x 20
for 0 < a <1 and 0<2< µ. X is then called a mixture density. Compute the hazard rate
hx(x) and show that lim hx(x) = 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc619cb67-aca3-4965-b7f6-4206faa9212f%2F0cdc02ac-1c92-4f46-a154-8c29a63ad423%2Fhx6252h_processed.png&w=3840&q=75)
Transcribed Image Text:1. Suppose that you generate 20 random samples from the integers {0,1, ...,9}. What are the
mean and variance for the number of integers that do not appear in the 20 samples?
2. Let X be a Poisson random variable with parameter 2. Show directly (i.e. don't use the
moment generating functions) that E[X"] = AE[(X + 1)"=1). Use the result to compute
E[X®].
3. Recall (from HW5) the hazard rate:
fx(x)
hx(x) =
%3D
1– Fx(x)'
Suppose that X is a continuous random variable with density
fx(x) = ade-* + (1 – a)µe¬#x, for x 20
for 0 < a <1 and 0<2< µ. X is then called a mixture density. Compute the hazard rate
hx(x) and show that lim hx(x) = 2.
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